Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
230 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 31. M16×C17 | Q8 | semidirect |
| 49. C4×Dic17 | Q8 | semidirect |
| 51. #63223 | Q8 | semidirect |
| 120. C17 | #2061 | semidirect |
| 129. M16 | Dic34 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763437 | 2 |
| #11762849 | 2 |
| #11762674 | 2 |
| #11762577 | 2 |
| #11762570 | 2 |
| #11762568 | 2 |
| C17×#428 | 2 |
| #2061 | 17 |